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t.BA.XXM1.AN1.19HS (Analysis 1)
Module: Analysis 1
This information was generated on: 09 November 2024
No.
t.BA.XXM1.AN1.19HS
Title
Analysis 1
Organised by
T IAMP
Credits
4
Description
Version: 4.0 start 01 August 2024
Short description
In this course, students learn the basic concepts of calculus of one real variable.
Module coordinator
Lichtensteiger Lukas (licn)
Learning objectives (competencies)
Objectives
Competences
Taxonomy levels
For polynomial type functions:
You understand the concepts of derivative and definite integral.
You conduct a curve discussion and calculate definite integrals using the main theorem.
F, M
K2
K3
You understand the concept of a sequence and calculate values of sequences that are given explicitly or recursively.
You show the convergence of a sequence using the limit definition.
You calculate limit values using symbolic methods.
F, M
K2, K3
K3
K3
You know the derivatives of the elementary functions.
You use the derivative rules, perform a curve discussion, and solve extreme value problems.
You use Newton's method to form recursion formulas.
F, M
K1
K2, K3
K3
Module contents
1. Concepts of differential and integral calculus
- Derivation (tangent, curve discussion)
- Antiderivatives and areas, main theorem for polynomials
2. Sequences, series (with sums) and limits
- Sequences (direct, recursive, arithmetic/geometric)
- Concept of limit values (arithmetic rules, limits of a function), continuity
- Series (arithmetic/geometric)
3. Extension of differential calculus
- Derivation of elementary functions
- Derivation rules
- Curve discussion
- Fractional rational functions (pole positions, liftable definition gaps, asymptotes)
- Extreme value problems
- Newton's method
Teaching materials
Notes and exercises distributed by lecturers, Moodle
Supplementary literature
Mathematik für Ingenieure und Naturwissenschaftler, Lothar Papula, Vieweg+Teubner
Mathematik, Tilo Arens et al., Springer Verlag
Prerequisites
Mathematik der technischen BM
Teaching language
German
Part of International Profile
No
Module structure
Type 3a
For more details please click on this link:
T_CL_Modulauspraegungen_SM2025
Exams
Description
Type
Form
Scope
Grade
Weighting
Graded assignments during teaching semester
regular assessments
written
max. 45 minutes each
grade
maximum 20%
End-of-semester exam
exam
written
90 minutes
grade
at least 80%
Remarks
During the first week of classes, a module agreement will be communicated which applies to all module courses and in which the exact number and scope of the graded assignments during the semester as well as the calculation method for the module grade are determined.
Legal basis
The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Note
Additional available versions:
1.0 start 01 February 2019
,
3.0 start 01 August 2021
Course: Analysis 1 - Praktikum
No.
t.BA.XXM1.AN1.19HS.P
Title
Analysis 1 - Praktikum
Note
No module description is available in the system for the cut-off date of 02 August 2099.
Course: Analysis 1 - Vorlesung
No.
t.BA.XXM1.AN1.19HS.V
Title
Analysis 1 - Vorlesung
Note
No module description is available in the system for the cut-off date of 02 August 2099.